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The bosses of several major supermarkets and fast food chains have waded into the Brexit debate, warning of higher prices and gaps on shelves if the UK leaves the EU without a deal in March.

In a letter to MPs, the chief executives of Sainsbury’s, Asda and the UK arms of McDonald’s and KFC said their “complex, just-in-time” supply chains would be “significantly disrupted in the event of no deal” as French officials impose customs checks in Calais.

The UK imports about a third of its food from the EU and even more during March, when many fruits and vegetables, including lettuce and tomatoes, are out of season, the letter says.